Symplectic model reduction of Hamiltonian systems using data-driven quadratic manifolds

Sharma, Harsh; Mu, Hongliang; Buchfink, Patrick; Geelen, Rudy; Glas, Silke; Kramer, Boris

doi:10.1016/j.cma.2023.116402

Title: Symplectic model reduction of Hamiltonian systems using data-driven quadratic manifolds

Journal Article · 01 December 2023 · Computer Methods in Applied Mechanics and Engineering

DOI: https://doi.org/10.1016/j.cma.2023.116402 · OSTI ID:1999944

; Mu, Hongliang;

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Sponsoring Organization:: USDOE

Grant/Contract Number:: SC0019303

OSTI ID:: 1999944

Journal Information:: Computer Methods in Applied Mechanics and Engineering, Journal Name: Computer Methods in Applied Mechanics and Engineering Vol. 417 Journal Issue: PA; ISSN 0045-7825

Publisher:: ElsevierCopyright Statement

Country of Publication:: Netherlands

Language:: English

References (45)

Model order reduction assisted by deep neural networks (ROM-net) Daniel, Thomas; Casenave, Fabien; Akkari, Nissrine Advanced Modeling and Simulation in Engineering Sciences, Vol. 7, Issue 1 https://doi.org/10.1186/s40323-020-00153-6	journal	April 2020
Nonlinear model order reduction based on local reduced-order bases: NONLINEAR MODEL REDUCTION BASED ON LOCAL REDUCED-ORDER BASES Amsallem, David; Zahr, Matthew J.; Farhat, Charbel International Journal for Numerical Methods in Engineering, Vol. 92, Issue 10 https://doi.org/10.1002/nme.4371	journal	June 2012
Dynamical reduced basis methods for Hamiltonian systems Pagliantini, Cecilia Numerische Mathematik, Vol. 148, Issue 2 https://doi.org/10.1007/s00211-021-01211-w	journal	June 2021
Performance assessment of energy-preserving, adaptive time-step variational integrators Sharma, Harsh; Borggaard, Jeff; Patil, Mayuresh Communications in Nonlinear Science and Numerical Simulation, Vol. 114 https://doi.org/10.1016/j.cnsns.2022.106646	journal	November 2022
Physics-informed cluster analysis and a priori efficiency criterion for the construction of local reduced-order bases Daniel, Thomas; Casenave, Fabien; Akkari, Nissrine Journal of Computational Physics, Vol. 458 https://doi.org/10.1016/j.jcp.2022.111120	journal	June 2022
Localized Discrete Empirical Interpolation Method Peherstorfer, Benjamin; Butnaru, Daniel; Willcox, Karen SIAM Journal on Scientific Computing, Vol. 36, Issue 1 https://doi.org/10.1137/130924408	journal	January 2014
Rank-adaptive structure-preserving model order reduction of Hamiltonian systems Hesthaven, Jan S.; Pagliantini, Cecilia; Ripamonti, Nicolò ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 56, Issue 2 https://doi.org/10.1051/m2an/2022013	journal	March 2022
Nonlinear reduced basis approximation of parameterized evolution equations via the method of freezing Ohlberger, Mario; Rave, Stephan Comptes Rendus Mathematique, Vol. 351, Issue 23-24 https://doi.org/10.1016/j.crma.2013.10.028	journal	December 2013
Data-driven operator inference for nonintrusive projection-based model reduction Peherstorfer, Benjamin; Willcox, Karen Computer Methods in Applied Mechanics and Engineering, Vol. 306 https://doi.org/10.1016/j.cma.2016.03.025	journal	July 2016
The Neural Network shifted-proper orthogonal decomposition: A machine learning approach for non-linear reduction of hyperbolic equations Papapicco, Davide; Demo, Nicola; Girfoglio, Michele Computer Methods in Applied Mechanics and Engineering, Vol. 392 https://doi.org/10.1016/j.cma.2022.114687	journal	March 2022
Symplectic Model Reduction of Hamiltonian Systems on Nonlinear Manifolds and Approximation with Weakly Symplectic Autoencoder Buchfink, Patrick; Glas, Silke; Haasdonk, Bernard SIAM Journal on Scientific Computing, Vol. 45, Issue 2 https://doi.org/10.1137/21M1466657	journal	March 2023
Predicting solar wind streams from the inner-heliosphere to Earth via shifted operator inference Issan, Opal; Kramer, Boris Journal of Computational Physics, Vol. 473 https://doi.org/10.1016/j.jcp.2022.111689	journal	January 2023
Quadratic approximation manifold for mitigating the Kolmogorov barrier in nonlinear projection-based model order reduction Barnett, Joshua; Farhat, Charbel Journal of Computational Physics, Vol. 464 https://doi.org/10.1016/j.jcp.2022.111348	journal	September 2022
A review of structure-preserving numerical methods for engineering applications Sharma, Harsh; Patil, Mayuresh; Woolsey, Craig Computer Methods in Applied Mechanics and Engineering, Vol. 366 https://doi.org/10.1016/j.cma.2020.113067	journal	July 2020
Structure-preserving Galerkin POD reduced-order modeling of Hamiltonian systems Gong, Yuezheng; Wang, Qi; Wang, Zhu Computer Methods in Applied Mechanics and Engineering, Vol. 315 https://doi.org/10.1016/j.cma.2016.11.016	journal	March 2017
Operator inference for non-intrusive model reduction with quadratic manifolds Geelen, Rudy; Wright, Stephen; Willcox, Karen Computer Methods in Applied Mechanics and Engineering, Vol. 403 https://doi.org/10.1016/j.cma.2022.115717	journal	January 2023
A linearly implicit energy-preserving exponential integrator for the nonlinear Klein-Gordon equation Jiang, Chaolong; Wang, Yushun; Cai, Wenjun Journal of Computational Physics, Vol. 419 https://doi.org/10.1016/j.jcp.2020.109690	journal	October 2020
Optimal Bases for Symplectic Model Order Reduction of Canonizable Linear Hamiltonian Systems Buchfink, Patrick; Glas, Silke; Haasdonk, Bernard IFAC-PapersOnLine, Vol. 55, Issue 20 https://doi.org/10.1016/j.ifacol.2022.09.138	journal	January 2022
Geometric Optimization for Structure-Preserving Model Reduction of Hamiltonian Systems Bendokat, Thomas; Zimmermann, Ralf IFAC-PapersOnLine, Vol. 55, Issue 20 https://doi.org/10.1016/j.ifacol.2022.09.137	journal	January 2022
Symplectic Model Reduction of Hamiltonian Systems Peng, Liqian; Mohseni, Kamran SIAM Journal on Scientific Computing, Vol. 38, Issue 1 https://doi.org/10.1137/140978922	journal	January 2016
Preserving energy resp. dissipation in numerical PDEs using the “Average Vector Field” method Celledoni, E.; Grimm, V.; McLachlan, R. I. Journal of Computational Physics, Vol. 231, Issue 20 https://doi.org/10.1016/j.jcp.2012.06.022	journal	August 2012
Non-intrusive reduced order modeling of natural convection in porous media using convolutional autoencoders: Comparison with linear subspace techniques Kadeethum, T.; Ballarin, F.; Choi, Y. Advances in Water Resources, Vol. 160 https://doi.org/10.1016/j.advwatres.2021.104098	journal	February 2022
Hamiltonian operator inference: Physics-preserving learning of reduced-order models for canonical Hamiltonian systems Sharma, Harsh; Wang, Zhu; Kramer, Boris Physica D: Nonlinear Phenomena, Vol. 431 https://doi.org/10.1016/j.physd.2021.133122	journal	March 2022
An artificial neural network framework for reduced order modeling of transient flows San, Omer; Maulik, Romit; Ahmed, Mansoor Communications in Nonlinear Science and Numerical Simulation, Vol. 77 https://doi.org/10.1016/j.cnsns.2019.04.025	journal	October 2019
The Differentiation of Pseudo-Inverses and Nonlinear Least Squares Problems Whose Variables Separate Golub, G. H.; Pereyra, V. SIAM Journal on Numerical Analysis, Vol. 10, Issue 2 https://doi.org/10.1137/0710036	journal	April 1973
Dynamically orthogonal field equations for continuous stochastic dynamical systems Sapsis, Themistoklis P.; Lermusiaux, Pierre F. J. Physica D: Nonlinear Phenomena, Vol. 238, Issue 23-24 https://doi.org/10.1016/j.physd.2009.09.017	journal	December 2009
Uber Die Beste Annaherung Von Funktionen Einer Gegebenen Funktionenklasse Kolmogoroff, A. The Annals of Mathematics, Vol. 37, Issue 1 https://doi.org/10.2307/1968691	journal	January 1936
Symplectic integration of Hamiltonian wave equations McLachlan, Robert Numerische Mathematik, Vol. 66, Issue 1 https://doi.org/10.1007/BF01385708	journal	December 1993
A Comprehensive Deep Learning-Based Approach to Reduced Order Modeling of Nonlinear Time-Dependent Parametrized PDEs Fresca, Stefania; Dede’, Luca; Manzoni, Andrea Journal of Scientific Computing, Vol. 87, Issue 2 https://doi.org/10.1007/s10915-021-01462-7	journal	April 2021
Symplectic integrators for Hamiltonian problems: an overview Sanz-Serna, J. M. Acta Numerica, Vol. 1 https://doi.org/10.1017/S0962492900002282	journal	January 1992
Nonlinear proper orthogonal decomposition for convection-dominated flows Ahmed, Shady E.; San, Omer; Rasheed, Adil Physics of Fluids, Vol. 33, Issue 12 https://doi.org/10.1063/5.0074310	journal	December 2021
Construction of higher order symplectic integrators Yoshida, Haruo Physics Letters A, Vol. 150, Issue 5-7 https://doi.org/10.1016/0375-9601(90)90092-3	journal	November 1990
Reduced basis techniques for nonlinear conservation laws Taddei, T.; Perotto, S.; Quarteroni, A. ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 49, Issue 3 https://doi.org/10.1051/m2an/2014054	journal	April 2015
A deep learning enabler for nonintrusive reduced order modeling of fluid flows Pawar, S.; Rahman, S. M.; Vaddireddy, H. Physics of Fluids, Vol. 31, Issue 8 https://doi.org/10.1063/1.5113494	journal	August 2019
A fast and accurate physics-informed neural network reduced order model with shallow masked autoencoder Kim, Youngkyu; Choi, Youngsoo; Widemann, David Journal of Computational Physics, Vol. 451 https://doi.org/10.1016/j.jcp.2021.110841	journal	February 2022
On the stability of symplectic and energy-momentum algorithms for non-linear Hamiltonian systems with symmetry Gonzalez, O.; Simo, J. C. Computer Methods in Applied Mechanics and Engineering, Vol. 134, Issue 3-4 https://doi.org/10.1016/0045-7825(96)01009-2	journal	August 1996
Localized non-intrusive reduced-order modelling in the operator inference framework Geelen, Rudy; Willcox, Karen Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 380, Issue 2229 https://doi.org/10.1098/rsta.2021.0206	journal	June 2022
Decay of the Kolmogorov N -width for wave problems Greif, Constantin; Urban, Karsten Applied Mathematics Letters, Vol. 96 https://doi.org/10.1016/j.aml.2019.05.013	journal	October 2019
Non-intrusive model reduction of large-scale, nonlinear dynamical systems using deep learning Gao, Han; Wang, Jian-Xun; Zahr, Matthew J. Physica D: Nonlinear Phenomena, Vol. 412 https://doi.org/10.1016/j.physd.2020.132614	journal	November 2020
Structure Preserving Model Reduction of Parametric Hamiltonian Systems Afkham, Babak Maboudi; Hesthaven, Jan S. SIAM Journal on Scientific Computing, Vol. 39, Issue 6 https://doi.org/10.1137/17M1111991	journal	January 2017
Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders Lee, Kookjin; Carlberg, Kevin T. Journal of Computational Physics https://doi.org/10.1016/j.jcp.2019.108973	journal	November 2019
POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition Fresca, Stefania; Manzoni, Andrea Computer Methods in Applied Mechanics and Engineering, Vol. 388 https://doi.org/10.1016/j.cma.2021.114181	journal	January 2022
Dynamical Low‐Rank Approximation Koch, Othmar; Lubich, Christian SIAM Journal on Matrix Analysis and Applications, Vol. 29, Issue 2 https://doi.org/10.1137/050639703	journal	January 2007
Efficient reduced models and a posteriori error estimation for parametrized dynamical systems by offline/online decomposition Haasdonk, Bernard; Ohlberger, Mario Mathematical and Computer Modelling of Dynamical Systems, Vol. 17, Issue 2 https://doi.org/10.1080/13873954.2010.514703	journal	March 2011
Structure-preserving reduced basis methods for Poisson systems Hesthaven, Jan S.; Pagliantini, Cecilia Mathematics of Computation, Vol. 90, Issue 330 https://doi.org/10.1090/mcom/3618	journal	April 2021

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